Simple (or not so simple) Momentum question

[rm446]

I've been thinking about basic momentum problems lately I'm having a surprising amount of trouble with one that didn't seem so bad at first glance.

Here's what I'm imagining: We've all heard of the simple momentum problem where a particle moving in the x direction at speed v1 runs into some unmoving object of a much much greater mass. Much like a basketball hitting the Earth, the particle simply bounces off in the negative x direction with the same speed v1.

Now here's the twist that's messing me up. Let's say the giant mass the particle is hitting is moving, but the movement is perpendicular to the particles initial velocity. So say the particle still has initial velocity v1 in the x direction but the giant mass has velocity v2 in the y direction. After the collision, is the particle going to have some velocity in the y direction or will it have the same result as the example I mentioned above?

Another way I've tried to think about it is what would happen if I dropped a basketball on the Earth from a car moving parallel to the Earth's surface? I mean I know what will happen in real life, but if there was no wind or ground friction, and the ball could not deform or rotate, then would it travel at the same speed as the car indefinitely?

Also when I try to do this on paper I find I'm one equation short, I have 2 conversation of momentum equations (for x and y) and conversation of energy, but I have 4 unknowns, the x and y components of speed for both objects (i.e. the basketball and Earth) after the collision.

 

[Drakkith]

Most likely the particle hitting the more massive object will be imparted with some of the perpendicular velocity after bouncing off. The more massive object would absorb some of the energy from the collision and would be pushed slightly in the direction that the particle initially was travelling.

Another way I've tried to think about it is what would happen if I dropped a basketball on the Earth from a car moving parallel to the Earth's surface? I mean I know what will happen in real life, but if there was no wind or ground friction, and the ball could not deform or rotate, then would it travel at the same speed as the car indefinitely?

With no friction it would bounce with the car forever. Without friction there would be no way to transfer some of the forward velocity of the ball to the Earth and cause it to slow down.

 

[rm446]

Thanks for the response. I'm still a little confused though, shouldn't the two examples have the exact same conclusion? I mean friction has no place in a particle collision right? If so,I believe the two problems are identical.

Anyways though I'm tempted to agree that any velocity gained in the particle/basketball by the massive object/Earth is either zero or negligible, but when I can't think of any reason why that should be certain and it's becoming like an itch I can't quite scratch. Even worse, when I tried putting this on paper it was easy to show that the affect of the basketball on the Earth was negligible, but there was nothing to even imply the affect of the Earth on the basketball is or isn't. The momentum equation for the direction of the Earth/massive object's movement when solved for the particle/basketball's final velocity is literally a very small number (the change in the Earth's velocity) times a very large number (the mass of the Earth divided by the mass of the basketball), there's nothing I can draw from that.

I assume these types of elastic collision of two particle questions are common in physics, but when I looked up my intro physics text each example provided some info about the particles after the collision. Is there some fourth relation I'm missing that would let me solve this out?

 

[Drakkith]

In particle collisions? I don't believe the standard use of friction applies to that honestly. I can't do the math for you, as I don't know it, but I can assure you that when the ball hits the ground it imparts some type of motion into the earth. It is so negligible it really isn't worth talking about usually though. Countering this is that you had to accelerate to get the ball up to speed in the first place, so no net loss of energy or velocity has been lost anywhere I don't think.

 

[Matterwave]

Momentum and energy conservation are, in general, not enough to solve a scattering problem. They merely provide some insight to the problem. Some knowledge of the forces involved is required.